
# Libraries to help with reading and manipulating data
import numpy as np
import pandas as pd

# Libraries to help with data visualization
import matplotlib.pyplot as plt
import seaborn as sns


sns.set()

# to split the data into train and test
from sklearn.model_selection import train_test_split

# to build linear regression_model
from sklearn.linear_model import LinearRegression

# to check model performance
from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score

# to build linear regression_model using statsmodels
import statsmodels.api as sm


df = pd.read_excel("Dataset - House Price Prediction.xlsx")  # uploading data


df.sample(n = 10)  # Finding random 10 rows


df.isna().sum()   #Checking missing values

cid                   0
dayhours              0
price                 0
room_bed            108
room_bath           108
living_measure       17
lot_measure          42
ceil                 42
coast                 1
sight                57
condition            57
quality               1
ceil_measure          1
basement              1
yr_built              1
yr_renovated          0
zipcode               0
lat                   0
long                  0
living_measure15    166
lot_measure15        29
furnished            29
total_area           29
dtype: int64


df.duplicated().sum() # Checking duplicate

0


f'Ther are {df.shape[0] } rows and  {df.shape[1]}'      # Checkig rows and columns

'Ther are 21613 rows and  23'


df["dayhours"].min() #Checking start data

'20140502T000000'


df["dayhours"].max() # Checking end data

'20150527T000000'


df.info() # Checking data type

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 21613 entries, 0 to 21612
Data columns (total 23 columns):
 #   Column            Non-Null Count  Dtype  
---  ------            --------------  -----  
 0   cid               21613 non-null  int64  
 1   dayhours          21613 non-null  object 
 2   price             21613 non-null  int64  
 3   room_bed          21505 non-null  float64
 4   room_bath         21505 non-null  float64
 5   living_measure    21596 non-null  float64
 6   lot_measure       21571 non-null  float64
 7   ceil              21571 non-null  object 
 8   coast             21612 non-null  object 
 9   sight             21556 non-null  float64
 10  condition         21556 non-null  object 
 11  quality           21612 non-null  float64
 12  ceil_measure      21612 non-null  float64
 13  basement          21612 non-null  float64
 14  yr_built          21612 non-null  object 
 15  yr_renovated      21613 non-null  int64  
 16  zipcode           21613 non-null  int64  
 17  lat               21613 non-null  float64
 18  long              21613 non-null  object 
 19  living_measure15  21447 non-null  float64
 20  lot_measure15     21584 non-null  float64
 21  furnished         21584 non-null  float64
 22  total_area        21584 non-null  object 
dtypes: float64(12), int64(4), object(7)
memory usage: 3.8+ MB


df = df[~df.isin(['$'])] # Removing symbol ($) from data


df.drop('cid', axis = 1, inplace = True)  # droping cid column


df.describe(include = 'all').T  # Data overview


df['year'] = df["dayhours"].astype(str).str.slice(0,4)       # extracting year from dayhours to a new column
df['month'] = df["dayhours"].astype(str).str.slice(4,6)       #extracting month from dayhours to a new column    
df['day'] = df["dayhours"].astype(str).str.slice(6,8)        #extraction day from dayhours to a new column
df.drop('dayhours', axis = 1)  # droping dayhours column


df[df.select_dtypes(['object']).columns] = df.select_dtypes(['object']).apply(lambda x: x.astype('category')) 
# Converting all object data types to category


def histogram_boxplot(data, feature, figsize=(12, 7), kde=False, bins=None):
    """
    Boxplot and histogram combined

    data: dataframe
    feature: dataframe column
    figsize: size of figure (default (12,7))
    kde: whether to show the density curve (default False)
    bins: number of bins for histogram (default None)
    """
    f2, (ax_box2, ax_hist2) = plt.subplots(
        nrows=2,  # Number of rows of the subplot grid= 2
        sharex=True,  # x-axis will be shared among all subplots
        gridspec_kw={"height_ratios": (0.25, 0.75)},
        figsize=figsize,
    )  # creating the 2 subplots
    sns.boxplot(
        data=data, x=feature, ax=ax_box2, showmeans=True, color="violet"
    )  # boxplot will be created and a star will indicate the mean value of the column
    sns.histplot(
        data=data, x=feature, kde=kde, ax=ax_hist2, bins=bins, palette="winter"
    ) if bins else sns.histplot(
        data=data, x=feature, kde=kde, ax=ax_hist2
    )  # For histogram
    ax_hist2.axvline(
        data[feature].mean(), color="green", linestyle="--"
    )  # Add mean to the histogram
    ax_hist2.axvline(
        data[feature].median(), color="black", linestyle="-"
    )  # Add median to the histogram


histogram_boxplot(df, "price")  # Checking price dristibution


histogram_boxplot(df, "room_bed") #distribution of room_bed


histogram_boxplot(df, "room_bath") #distribution of room_bath


histogram_boxplot(df, "living_measure") # distribution of living measure


histogram_boxplot(df, "lot_measure") #distribution of lot_measure


histogram_boxplot(df, "sight") # checking distribution of sight


histogram_boxplot(df, "quality") #checking distribution of quality


histogram_boxplot(df, "ceil_measure")  # Checking distribution of ceil measure


histogram_boxplot(df, "basement") #checking distribution of basement


histogram_boxplot(df, "lat")  # checking distribution of lat


# function to create labeled barplots


def labeled_barplot(data, feature, perc=False, n=None):
    """
    Barplot with percentage at the top

    data: dataframe
    feature: dataframe column
    perc: whether to display percentages instead of count (default is False)
    n: displays the top n category levels (default is None, i.e., display all levels)
    """

    total = len(data[feature])  # length of the column
    count = data[feature].nunique()
    if n is None:
        plt.figure(figsize=(count + 1, 5))
    else:
        plt.figure(figsize=(n + 1, 5))

    plt.xticks(rotation=90, fontsize=15)
    ax = sns.countplot(
        data=data,
        x=feature,
        palette="Paired",
        order=data[feature].value_counts().index[:n].sort_values(),
    )

    for p in ax.patches:
        if perc == True:
            label = "{:.1f}%".format(
                100 * p.get_height() / total
            )  # percentage of each class of the category
        else:
            label = p.get_height()  # count of each level of the category

        x = p.get_x() + p.get_width() / 2  # width of the plot
        y = p.get_height()  # height of the plot

        ax.annotate(
            label,
            (x, y),
            ha="center",
            va="center",
            size=12,
            xytext=(0, 5),
            textcoords="offset points",
        )  # annotate the percentage

    plt.show()  # show the plot


labeled_barplot(df, "year")   #bar plot of year


labeled_barplot(df, "month", perc = True)  #bar plot of month showing percentages of houses sold


labeled_barplot(df, "ceil", perc = True); #Checking count of ceil or floors in houses


labeled_barplot(df, "coast", perc = True), #checking whether houses are on the coast

(None,)


labeled_barplot(df, "condition", perc = True)   #barplot of condition showing percentages


labeled_barplot(df, "coast", perc = True) #bar plot of coast


plt.figure(figsize=(10, 7))            
sns.heatmap(
    df.corr(), annot=True, vmin=-1, vmax=1, fmt=".2f", cmap="Spectral",
);
# Finding the correlation between numberic attributes


sns.pairplot(df,  kind = 'scatter', diag_kind = 'auto'); #pair plot of all numeric attributes


# function to plot stacked bar chart


def stacked_barplot(data, predictor, target):
    """
    Print the category counts and plot a stacked bar chart

    data: dataframe
    predictor: independent variable
    target: target variable
    """
    count = data[predictor].nunique()
    sorter = data[target].value_counts().index[-1]
    tab1 = pd.crosstab(data[predictor], data[target], margins=True).sort_values(
        by=sorter, ascending=False
    )
    print(tab1)
    print("-" * 120)
    tab = pd.crosstab(data[predictor], data[target], normalize="index").sort_values(
        by=sorter, ascending=False
    )
    tab.plot(kind="bar", stacked=True, figsize=(count + 1, 5))
    plt.legend(
        loc="lower left",
        frameon=False,
    )
    plt.legend(loc="upper left", bbox_to_anchor=(1, 1))
    plt.show()


plt.figure(figsize = (10,20))
sns.boxplot(x = 'year',y = 'price', showmeans = True, data = df); #year vs price
plt.show()


sns.boxplot(x = 'coast',y = 'price', showmeans=True, data = df); #, finding prices in coastal and non coastal);
plt.show()


plt.figure(figsize=(5, 8))
sns.boxplot(x = 'furnished',y = 'price', showmeans=True,  data = df); 
plt.show()


plt.figure (figsize = (10, 8))
sns.boxplot(x = 'condition',y = 'price', showmeans=True, data = df); #, hue = 'day_of_the_week');
plt.show()


plt.figure(figsize=(12, 8))
sns.lineplot(data=df, x="month", y="price")     #Plotting to find average home prices for each month

<AxesSubplot:xlabel='month', ylabel='price'>


df.groupby("month")['price'].mean() # Checking avarage prices for each month

month
01    525963.251534
02    507919.603200
03    544057.683200
04    561933.463021
05    550849.746893
06    558123.736239
07    544892.161013
08    536527.039691
09    529315.868095
10    539127.477636
11    522058.861800
12    524602.893270
Name: price, dtype: float64


plt.figure(figsize=(10, 4))
sns.boxplot(data=df, x= "sight", y="price")  # Code to find price vs sight
plt.xticks(rotation = 90);


plt.figure(figsize=(20, 8))
plt.xticks(rotation = 90)
sns.boxplot(data=df, x= "yr_built", y="price");  # Code to find price vs sight


plt.figure(figsize=(30, 10))
plt.xticks(rotation = 90)
sns.boxplot(data=df, x= "yr_renovated", y="price"); # Ploting  price vs year_renovated


plt.figure(figsize=(30, 4))
sns.boxplot(data=df, x= "zipcode", y="price")
plt.xticks(rotation = 90);


percent_renovated = df[df['yr_renovated']>0].shape[0]     # Finding number of houses renovated
f'{percent_renovated}  of the 21613 were renovated, making {(percent_renovated)/df.shape[0]*100}% of houses renovated'

'914  of the 21613 were renovated, making 4.228936288344977% of houses renovated'


df.info() # Finding data type

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 21613 entries, 0 to 21612
Data columns (total 25 columns):
 #   Column            Non-Null Count  Dtype   
---  ------            --------------  -----   
 0   dayhours          21613 non-null  category
 1   price             21613 non-null  int64   
 2   room_bed          21505 non-null  float64 
 3   room_bath         21505 non-null  float64 
 4   living_measure    21596 non-null  float64 
 5   lot_measure       21571 non-null  float64 
 6   ceil              21541 non-null  category
 7   coast             21582 non-null  category
 8   sight             21556 non-null  float64 
 9   condition         21528 non-null  category
 10  quality           21612 non-null  float64 
 11  ceil_measure      21612 non-null  float64 
 12  basement          21612 non-null  float64 
 13  yr_built          21598 non-null  category
 14  yr_renovated      21613 non-null  int64   
 15  zipcode           21613 non-null  int64   
 16  lat               21613 non-null  float64 
 17  long              21579 non-null  category
 18  living_measure15  21447 non-null  float64 
 19  lot_measure15     21584 non-null  float64 
 20  furnished         21584 non-null  float64 
 21  total_area        21545 non-null  category
 22  year              21613 non-null  category
 23  month             21613 non-null  category
 24  day               21613 non-null  category
dtypes: category(10), float64(12), int64(3)
memory usage: 3.1 MB


df['ceil']= df['ceil'].astype(float)
df['condition']= df['condition'].astype(float)
df['yr_built']= df['yr_built'].astype(float)
df["total_area"]=df['total_area'].astype(float)
df["year"]=df['year'].astype(float)


# counting the number of missing values per row
df.isnull().sum()

dayhours              0
price                 0
room_bed            108
room_bath           108
living_measure       17
lot_measure          42
ceil                 72
coast                31
sight                57
condition            85
quality               1
ceil_measure          1
basement              1
yr_built             15
yr_renovated          0
zipcode               0
lat                   0
long                 34
living_measure15    166
lot_measure15        29
furnished            29
total_area           68
year                  0
month                 0
day                   0
dtype: int64


df["yr_renovated"].replace(0, df["yr_built"].median(), inplace = True)


df1 = df.fillna(df.median())  # Filling all missing values with median


df1.sample(n = 10)  # Checking ten random rows


df1.isna().sum() # Finding missing value

dayhours             0
price                0
room_bed             0
room_bath            0
living_measure       0
lot_measure          0
ceil                 0
coast               31
sight                0
condition            0
quality              0
ceil_measure         0
basement             0
yr_built             0
yr_renovated         0
zipcode              0
lat                  0
long                34
living_measure15     0
lot_measure15        0
furnished            0
total_area           0
year                 0
month                0
day                  0
dtype: int64


df1["zipcode"]= df1["zipcode"].astype(str).str.slice(0,3)  # extracting just first 3 digit of zipcode
df1['zipcode'] = pd.Categorical(df1.zipcode)     # converting data type to categorical
df1.dtypes

dayhours            category
price                  int64
room_bed             float64
room_bath            float64
living_measure       float64
lot_measure          float64
ceil                 float64
coast               category
sight                float64
condition            float64
quality              float64
ceil_measure         float64
basement             float64
yr_built             float64
yr_renovated           int64
zipcode             category
lat                  float64
long                category
living_measure15     float64
lot_measure15        float64
furnished            float64
total_area           float64
year                 float64
month               category
day                 category
dtype: object


df1["lat"]=df["lat"].astype(str).str.slice(3,7).astype("float")
df1["long"]=df["long"].astype(str).str.slice(5,8).astype("float")
df1


df1["furnished"]=df1["furnished"].astype("category")
df1["sight"]=df1["sight"].astype("category")


df1.info() # Finding data types

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 21613 entries, 0 to 21612
Data columns (total 25 columns):
 #   Column            Non-Null Count  Dtype   
---  ------            --------------  -----   
 0   dayhours          21613 non-null  category
 1   price             21613 non-null  int64   
 2   room_bed          21613 non-null  float64 
 3   room_bath         21613 non-null  float64 
 4   living_measure    21613 non-null  float64 
 5   lot_measure       21613 non-null  float64 
 6   ceil              21613 non-null  float64 
 7   coast             21582 non-null  category
 8   sight             21613 non-null  category
 9   condition         21613 non-null  float64 
 10  quality           21613 non-null  float64 
 11  ceil_measure      21613 non-null  float64 
 12  basement          21613 non-null  float64 
 13  yr_built          21613 non-null  float64 
 14  yr_renovated      21613 non-null  int64   
 15  zipcode           21613 non-null  category
 16  lat               21613 non-null  float64 
 17  long              21579 non-null  float64 
 18  living_measure15  21613 non-null  float64 
 19  lot_measure15     21613 non-null  float64 
 20  furnished         21613 non-null  category
 21  total_area        21613 non-null  float64 
 22  year              21613 non-null  float64 
 23  month             21613 non-null  category
 24  day               21613 non-null  category
dtypes: category(7), float64(16), int64(2)
memory usage: 3.1 MB


df1.dropna(inplace = True)  # 34 rows with missing values


df1.isna().sum() #Finding missing values

dayhours            0
price               0
room_bed            0
room_bath           0
living_measure      0
lot_measure         0
ceil                0
coast               0
sight               0
condition           0
quality             0
ceil_measure        0
basement            0
yr_built            0
yr_renovated        0
zipcode             0
lat                 0
long                0
living_measure15    0
lot_measure15       0
furnished           0
total_area          0
year                0
month               0
day                 0
dtype: int64


df1["house_age"] = df1['year']- df1['yr_built']
df1["renovation_age"] = df1['year']- df1['yr_renovated']


df1["logprice"] = np.log(df1["price"])


df1.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 21548 entries, 0 to 21612
Data columns (total 28 columns):
 #   Column            Non-Null Count  Dtype   
---  ------            --------------  -----   
 0   dayhours          21548 non-null  category
 1   price             21548 non-null  int64   
 2   room_bed          21548 non-null  float64 
 3   room_bath         21548 non-null  float64 
 4   living_measure    21548 non-null  float64 
 5   lot_measure       21548 non-null  float64 
 6   ceil              21548 non-null  float64 
 7   coast             21548 non-null  category
 8   sight             21548 non-null  category
 9   condition         21548 non-null  float64 
 10  quality           21548 non-null  float64 
 11  ceil_measure      21548 non-null  float64 
 12  basement          21548 non-null  float64 
 13  yr_built          21548 non-null  float64 
 14  yr_renovated      21548 non-null  int64   
 15  zipcode           21548 non-null  category
 16  lat               21548 non-null  float64 
 17  long              21548 non-null  float64 
 18  living_measure15  21548 non-null  float64 
 19  lot_measure15     21548 non-null  float64 
 20  furnished         21548 non-null  category
 21  total_area        21548 non-null  float64 
 22  year              21548 non-null  float64 
 23  month             21548 non-null  category
 24  day               21548 non-null  category
 25  house_age         21548 non-null  float64 
 26  renovation_age    21548 non-null  float64 
 27  logprice          21548 non-null  float64 
dtypes: category(7), float64(19), int64(2)
memory usage: 3.8 MB


#Dropping unwanted columns
df2 = df1.drop(["dayhours", 'year', 'yr_built',"yr_renovated", "day", "price"], axis = 1 )


df2.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 21548 entries, 0 to 21612
Data columns (total 22 columns):
 #   Column            Non-Null Count  Dtype   
---  ------            --------------  -----   
 0   room_bed          21548 non-null  float64 
 1   room_bath         21548 non-null  float64 
 2   living_measure    21548 non-null  float64 
 3   lot_measure       21548 non-null  float64 
 4   ceil              21548 non-null  float64 
 5   coast             21548 non-null  category
 6   sight             21548 non-null  category
 7   condition         21548 non-null  float64 
 8   quality           21548 non-null  float64 
 9   ceil_measure      21548 non-null  float64 
 10  basement          21548 non-null  float64 
 11  zipcode           21548 non-null  category
 12  lat               21548 non-null  float64 
 13  long              21548 non-null  float64 
 14  living_measure15  21548 non-null  float64 
 15  lot_measure15     21548 non-null  float64 
 16  furnished         21548 non-null  category
 17  total_area        21548 non-null  float64 
 18  month             21548 non-null  category
 19  house_age         21548 non-null  float64 
 20  renovation_age    21548 non-null  float64 
 21  logprice          21548 non-null  float64 
dtypes: category(5), float64(17)
memory usage: 3.1 MB


numeric_columns = df2.select_dtypes(include=np.number).columns.tolist()
#numeric_columns.remove(["lat", "long"])  # dropping year column as it is temporal variable


# let's plot the boxplots of all columns to check for outliers
plt.figure(figsize=(20, 30))

for i, variable in enumerate(numeric_columns):
    plt.subplot(5, 4, i + 1)
    plt.boxplot(df2[variable], whis=1.5)
    plt.tight_layout()
    plt.title(variable)

plt.show()

df2


def treat_outliers(df2, col):
    """
    treats outliers in a variable
    col: str, name of the numerical variable
    df: dataframe
    col: name of the column
    """
    Q1 = df2[col].quantile(0.25)  # 25th quantile
    Q3 = df2[col].quantile(0.75)  # 75th quantile
    IQR = Q3 - Q1
    Lower_Whisker = Q1 - 1.5 * IQR
    Upper_Whisker = Q3 + 1.5 * IQR

    # all the values smaller than Lower_Whisker will be assigned the value of Lower_Whisker
    # all the values greater than Upper_Whisker will be assigned the value of Upper_Whisker
    df2[col] = np.clip(df2[col], Lower_Whisker, Upper_Whisker)

    return df2


def treat_outliers_all(df2, col_list):
    """
    treat outlier in all numerical variables
    col_list: list of numerical variables
    df: data frame
    """
    for c in col_list:
        df = treat_outliers(df2, c)

    return df2


# treating the outliers
numerical_col = df2.select_dtypes(include=np.number).columns.tolist()
df2 = treat_outliers_all(df2, numerical_col)


# let's look at the boxplots to see if the outliers have been treated or not
plt.figure(figsize=(20, 30))

for i, variable in enumerate(numeric_columns):
    plt.subplot(5, 4, i + 1)
    plt.boxplot(df2[variable], whis=1.5)
    plt.tight_layout()
    plt.title(variable)

plt.show()


histogram_boxplot(df2, "logprice")  # Checking dristibution of the logprice without outliers


histogram_boxplot(df2, "living_measure") # distribution of living measure without outliers


plt.figure(figsize = (10,5))
sns.boxplot(x = 'coast',y = 'room_bath', showmeans = True,  data = df2); # boxplot of room_bath at  coast(1) and non coast(0) houses.
plt.show()


plt.figure(figsize = (10,8))
sns.boxplot(x = 'zipcode',y = 'logprice', showmeans = True,  data = df2); # boxplot of prices at two different areas. numbers represnt first3 digit of zipoce
plt.show()


labeled_barplot(df2, "coast", perc = True) #bar plot of coast


labeled_barplot(df2, "furnished", perc = True); #bar plot of coast

C:\Users\eadogla\Anaconda3\Anaconda1\lib\site-packages\pandas\io\formats\format.py:1405: FutureWarning: Index.ravel returning ndarray is deprecated; in a future version this will return a view on self.
  for val, m in zip(values.ravel(), mask.ravel())


plt.figure(figsize=(10, 7))            
sns.heatmap(
    df2.corr(), annot=True, vmin=-1, vmax=1, fmt=".2f", cmap="Spectral",
);
# Finding the correlation between numberic attributes without their outliers


plt.figure(figsize=(8, 5))
sns.boxplot(data=df2, x= "coast", showmeans = True,  y="logprice")  # Code to find price vs sight
plt.xticks(rotation = 90);


plt.figure(figsize=(8, 5))
sns.boxplot(data=df2, x= "furnished", showmeans = True,  y="logprice");  # Code to find price vs sight
plt.xticks(rotation = 90);

C:\Users\eadogla\Anaconda3\Anaconda1\lib\site-packages\pandas\io\formats\format.py:1405: FutureWarning: Index.ravel returning ndarray is deprecated; in a future version this will return a view on self.
  for val, m in zip(values.ravel(), mask.ravel())


plt.figure(figsize=(12, 8))
sns.lineplot(data=df2, x="month", y="logprice")     #Plotting to find  trend of log of average home prices for each month

<AxesSubplot:xlabel='month', ylabel='logprice'>


plt.figure(figsize=(12, 8))
sns.lineplot(data=df2, x="quality", y="logprice");     #Plotting to find  trend of log of average home prices for each month


plt.figure(figsize=(12, 8))
sns.lineplot(data=df2, x="condition", y="logprice");     #Plotting to find  trend of log of average home prices for each condition


plt.figure(figsize=(12, 8))
sns.regplot(data=df2, x="lat", y="logprice");


# function to plot stacked bar chart


def stacked_barplot(data, predictor, target):
    """
    Print the category counts and plot a stacked bar chart

    data: dataframe
    predictor: independent variable
    target: target variable
    """
    count = data[predictor].nunique()
    sorter = data[target].value_counts().index[-1]
    tab1 = pd.crosstab(data[predictor], data[target], margins=True).sort_values(
        by=sorter, ascending=False
    )
    print(tab1)
    print("-" * 12)
    tab = pd.crosstab(data[predictor], data[target], normalize="index").sort_values(
        by=sorter, ascending=False
    )
    tab.plot(kind="bar", stacked=True, figsize=(count + 5, 6))
    plt.legend(
        loc="lower left", frameon=False,
    )
    plt.legend(loc="upper left", bbox_to_anchor=(1, 1))
    plt.show()


stacked_barplot(df2, "condition", "zipcode")

zipcode      980   981    All
condition                    
All        12600  8948  21548
3.0         8274  5746  14020
4.0         3503  2139   5642
5.0          734   951   1685
2.0           78    93    171
1.5           11    19     30
------------


stacked_barplot(df2, "zipcode", "furnished"), #Stacked barplot of houses furnished and unfurnished at two starting zipcodes

furnished    0.0   1.0    All
zipcode                      
All        17314  4234  21548
980         9328  3272  12600
981         7986   962   8948
------------

(None,)


stacked_barplot(df2, "sight", "furnished")

furnished    0.0   1.0    All
sight                        
All        17314  4234  21548
0.0        16141  3298  19439
2.0          592   364    956
3.0          238   267    505
4.0          120   196    316
1.0          223   109    332
------------


stacked_barplot(df2, "coast", "zipcode")

zipcode    980   981    All
coast                      
All      12600  8948  21548
0        12511  8876  21387
1           89    72    161
------------


# defining X and y variables
X = df2.drop(["logprice"], axis=1)
y = df2["logprice"]

print(X.head())
print(y.head())

   room_bed  room_bath  living_measure  lot_measure  ceil coast sight  \
0       4.0       1.75          3050.0       9440.0   1.0     0   0.0   
1       2.0       1.00           670.0       3101.0   1.0     0   0.0   
2       4.0       2.75          3040.0       2415.0   2.0     1   4.0   
3       3.0       2.50          1740.0       3721.0   2.0     0   0.0   
4       2.0       1.00          1120.0       4590.0   1.0     0   0.0   

   condition  quality  ceil_measure  ...  zipcode     lat   long  \
0        3.0      8.0        1800.0  ...      980  7228.0  183.0   
1        4.0      6.0         670.0  ...      981  5546.0  274.0   
2        3.0      8.0        3040.0  ...      981  5188.0  256.0   
3        3.0      8.0        1740.0  ...      980  3363.0  213.0   
4        3.0      7.0        1120.0  ...      981  5663.0  285.0   

   living_measure15  lot_measure15  furnished total_area  month house_age  \
0            2020.0         8660.0        0.0    12490.0     04      49.0   
1            1660.0         4100.0        0.0     3771.0     03      67.0   
2            2620.0         2433.0        0.0     5455.0     08      48.0   
3            2030.0         3794.0        0.0     5461.0     10       5.0   
4            1120.0         5100.0        0.0     5710.0     02      91.0   

   renovation_age  
0            40.0  
1            40.0  
2            39.0  
3            39.0  
4            40.0  

[5 rows x 21 columns]
0    13.304685
1    12.154779
2    13.507626
3    12.456831
4    13.017003
Name: logprice, dtype: float64


X = pd.get_dummies(
    X,
    columns=X.select_dtypes(include=["object", "category"]).columns.tolist(),
    drop_first=True,
)
X.head()


# splitting the data in 70:30 ratio for train to test data

x_train, x_test, y_train, y_test = train_test_split(
    X, y, test_size=0.3, random_state=42
)


print("Number of rows in train data =", x_train.shape[0])
print("Number of rows in test data =", x_test.shape[0])

Number of rows in train data = 15083
Number of rows in test data = 6465


# fitting the model on the train data (70% of the whole data)
from sklearn.linear_model import LinearRegression

linearregression = LinearRegression()
linearregression.fit(x_train, y_train)

LinearRegression()


coef_df = pd.DataFrame(
    np.append(linearregression.coef_, linearregression.intercept_),
    index=x_train.columns.tolist() + ["Intercept"],
    columns=["Coefficients"],
)

coef_df


# function to compute adjusted R-squared
def adj_r2_score(predictors, targets, predictions):
    r2 = r2_score(targets, predictions)
    n = predictors.shape[0]
    k = predictors.shape[1]
    return 1 - ((1 - r2) * (n - 1) / (n - k - 1))


# function to compute MAPE
def mape_score(targets, predictions):
    return np.mean(np.abs(targets - predictions) / targets) * 100


# function to compute different metrics to check performance of a regression model
def model_performance_regression(model, predictors, target):
    """
    Function to compute different metrics to check regression model performance

    model: regressor
    predictors: independent variables
    target: dependent variable
    """

    # predicting using the independent variables
    pred = model.predict(predictors)

    r2 = r2_score(target, pred)  # to compute R-squared
    adjr2 = adj_r2_score(predictors, target, pred)  # to compute adjusted R-squared
    rmse = np.sqrt(mean_squared_error(target, pred))  # to compute RMSE
    mae = mean_absolute_error(target, pred)  # to compute MAE
    mape = mape_score(target, pred)  # to compute MAPE

    # creating a dataframe of metrics
    df_perf = pd.DataFrame(
        {
            "RMSE": rmse,
            "MAE": mae,
            "R-squared": r2,
            "Adj. R-squared": adjr2,
            "MAPE": mape,
        },
        index=[0],
    )

    return df_perf


# checking model performance on train set (seen 70% data)
print("Training Performance\n")
linearregression_train_perf = model_performance_regression(
    linearregression, x_train, y_train
)
linearregression_train_perf

Training Performance


# checking model performance on test set (seen 30% data)
print("Test Performance\n")
linearregression_test_perf = model_performance_regression(
    linearregression, x_test, y_test
)
linearregression_test_perf

Test Performance


# unlike sklearn, statsmodels does not add a constant to the data on its own
# we have to add the constant manually
x_train1 = sm.add_constant(x_train)
# adding constant to the test data
x_test1 = sm.add_constant(x_test)

olsmod0 = sm.OLS(y_train, x_train1).fit()
print(olsmod0.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               logprice   R-squared:                       0.700
Model:                            OLS   Adj. R-squared:                  0.700
Method:                 Least Squares   F-statistic:                     1034.
Date:                Sun, 03 Apr 2022   Prob (F-statistic):               0.00
Time:                        19:26:47   Log-Likelihood:                -2275.4
No. Observations:               15083   AIC:                             4621.
Df Residuals:                   15048   BIC:                             4888.
Df Model:                          34                                         
Covariance Type:            nonrobust                                         
====================================================================================
                       coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------
const               10.9119      0.239     45.591      0.000      10.443      11.381
room_bed            -0.0329      0.004     -9.091      0.000      -0.040      -0.026
room_bath            0.0686      0.006     11.724      0.000       0.057       0.080
living_measure       0.0002   2.42e-05      7.777      0.000       0.000       0.000
lot_measure      -1.499e-05    4.6e-06     -3.256      0.001    -2.4e-05   -5.96e-06
ceil                 0.0402      0.007      6.088      0.000       0.027       0.053
condition            0.0566      0.004     14.220      0.000       0.049       0.064
quality              0.2030      0.005     41.618      0.000       0.193       0.213
ceil_measure     -6.494e-06   2.48e-05     -0.262      0.793    -5.5e-05    4.21e-05
basement         -4.771e-06   2.42e-05     -0.197      0.844   -5.23e-05    4.27e-05
lat               4.954e-05   1.16e-06     42.539      0.000    4.73e-05    5.18e-05
long             -3.101e-05   1.45e-05     -2.131      0.033   -5.95e-05   -2.49e-06
living_measure15     0.0001   6.24e-06     21.197      0.000       0.000       0.000
lot_measure15    -6.477e-06   1.29e-06     -5.005      0.000   -9.01e-06   -3.94e-06
total_area        1.487e-05    4.5e-06      3.306      0.001    6.05e-06    2.37e-05
house_age            0.0040      0.000     32.411      0.000       0.004       0.004
renovation_age      -0.0203      0.006     -3.453      0.001      -0.032      -0.009
coast_1              0.2999      0.033      9.173      0.000       0.236       0.364
sight_1.0            0.1097      0.019      5.801      0.000       0.073       0.147
sight_2.0            0.0919      0.012      7.920      0.000       0.069       0.115
sight_3.0            0.1048      0.016      6.604      0.000       0.074       0.136
sight_4.0            0.2168      0.024      9.092      0.000       0.170       0.264
zipcode_981          0.0948      0.007     14.281      0.000       0.082       0.108
furnished_1.0       -0.0139      0.010     -1.403      0.160      -0.033       0.006
month_02             0.0285      0.014      1.966      0.049    8.64e-05       0.057
month_03             0.0648      0.013      4.852      0.000       0.039       0.091
month_04             0.0865      0.013      6.678      0.000       0.061       0.112
month_05             0.0302      0.013      2.243      0.025       0.004       0.057
month_06             0.0072      0.014      0.510      0.610      -0.021       0.035
month_07             0.0049      0.014      0.346      0.729      -0.023       0.033
month_08             0.0169      0.014      1.168      0.243      -0.011       0.045
month_09            -0.0082      0.015     -0.561      0.575      -0.037       0.020
month_10            -0.0038      0.014     -0.259      0.796      -0.032       0.025
month_11            -0.0097      0.015     -0.640      0.522      -0.039       0.020
month_12            -0.0018      0.015     -0.120      0.904      -0.031       0.028
==============================================================================
Omnibus:                      116.070   Durbin-Watson:                   2.018
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              149.416
Skew:                           0.126   Prob(JB):                     3.59e-33
Kurtosis:                       3.417   Cond. No.                     1.99e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.99e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


from statsmodels.stats.outliers_influence import variance_inflation_factor

# we will define a function to check VIF
def checking_vif(predictors):
    vif = pd.DataFrame()
    vif["feature"] = predictors.columns

    # calculating VIF for each feature
    vif["VIF"] = [
        variance_inflation_factor(predictors.values, i)
        for i in range(len(predictors.columns))
    ]
    return vif


checking_vif(x_train1)


def treating_multicollinearity(predictors, target, high_vif_columns):
    """
    Checking the effect of dropping the columns showing high multicollinearity
    on model performance (adj. R-squared and RMSE)

    predictors: independent variables
    target: dependent variable
    high_vif_columns: columns having high VIF
    """
    # empty lists to store adj. R-squared and RMSE values
    adj_r2 = []
    rmse = []

    # build ols models by dropping one of the high VIF columns at a time
    # store the adjusted R-squared and RMSE in the lists defined previously
    for cols in high_vif_columns:
        # defining the new train set
        train = predictors.loc[:, ~predictors.columns.str.startswith(cols)]

        # create the model
        olsmodel = sm.OLS(target, train).fit()

        # adding adj. R-squared and RMSE to the lists
        adj_r2.append(olsmodel.rsquared_adj)
        rmse.append(np.sqrt(olsmodel.mse_resid))

    # creating a dataframe for the results
    temp = pd.DataFrame(
        {
            "col": high_vif_columns,
            "Adj. R-squared after_dropping col": adj_r2,
            "RMSE after dropping col": rmse,
        }
    ).sort_values(by="Adj. R-squared after_dropping col", ascending=False)
    temp.reset_index(drop=True, inplace=True)

    return temp


col_list = [
    "living_measure",
    "lot_measure",
    "ceil_measure",
    "basement", "lot_measure15", "total_area"
]

res = treating_multicollinearity(x_train1, y_train, col_list)
res


col_to_drop = "basement"
x_train2 = x_train1.loc[:, ~x_train1.columns.str.startswith(col_to_drop)]
x_test2 = x_test1.loc[:, ~x_test1.columns.str.startswith(col_to_drop)]

# Check VIF now
vif = checking_vif(x_train2)
print("VIF after dropping ", col_to_drop)
vif

VIF after dropping  basement


col_list = [
     "living_measure",
    "lot_measure",
    "ceil_measure",
    "lot_measure15", "total_area"
]

res = treating_multicollinearity(x_train2, y_train, col_list)
res


col_to_drop = "ceil_measure"
x_train3 = x_train2.loc[:, ~x_train2.columns.str.startswith(col_to_drop)]
x_test3 = x_test2.loc[:, ~x_test2.columns.str.startswith(col_to_drop)]

# Check VIF now
vif = checking_vif(x_train3)
print("VIF after dropping ", col_to_drop)
vif

VIF after dropping  ceil_measure


col_list = [
         "lot_measure",
    "lot_measure15", "total_area","living_measure"
]

res = treating_multicollinearity(x_train3, y_train, col_list)
res


col_to_drop = "total_area"  
x_train4 = x_train3.loc[:, ~x_train3.columns.str.startswith(col_to_drop)]
x_test4 = x_test3.loc[:, ~x_test3.columns.str.startswith(col_to_drop)]

# Check VIF now
vif = checking_vif(x_train4)
print("VIF after dropping ", col_to_drop)
vif

VIF after dropping  total_area


col_list = ["living_measure", "lot_measure", "lot_measure15"
         
]

res = treating_multicollinearity(x_train3, y_train, col_list)
res


col_to_drop = "lot_measure15"
x_train5 = x_train4.loc[:, ~x_train4.columns.str.startswith(col_to_drop)]
x_test5 = x_test4.loc[:, ~x_test4.columns.str.startswith(col_to_drop)]

# Check VIF now
vif = checking_vif(x_train5)
print("VIF after dropping ", col_to_drop)
vif

VIF after dropping  lot_measure15


col_list = ["living_measure"]
         


res = treating_multicollinearity(x_train5, y_train, col_list)
res


col_to_drop = "living_measure"
x_train6 = x_train5.loc[:, ~x_train5.columns.str.startswith(col_to_drop)]
x_test6 = x_test5.loc[:, ~x_test5.columns.str.startswith(col_to_drop)]

# Check VIF now
vif = checking_vif(x_train6)
print("VIF after dropping ", col_to_drop)
vif

VIF after dropping  living_measure


olsmod1 = sm.OLS(y_train, x_train6).fit()
print(olsmod1.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               logprice   R-squared:                       0.657
Model:                            OLS   Adj. R-squared:                  0.656
Method:                 Least Squares   F-statistic:                     1028.
Date:                Sun, 03 Apr 2022   Prob (F-statistic):               0.00
Time:                        19:26:54   Log-Likelihood:                -3301.5
No. Observations:               15083   AIC:                             6661.
Df Residuals:                   15054   BIC:                             6882.
Df Model:                          28                                         
Covariance Type:            nonrobust                                         
==================================================================================
                     coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------
const              9.9018      0.255     38.852      0.000       9.402      10.401
room_bed           0.0244      0.004      6.885      0.000       0.017       0.031
room_bath          0.1734      0.006     31.219      0.000       0.162       0.184
lot_measure     3.213e-06   5.98e-07      5.372      0.000    2.04e-06    4.39e-06
ceil               0.0533      0.006      8.702      0.000       0.041       0.065
condition          0.0491      0.004     11.610      0.000       0.041       0.057
quality            0.2782      0.005     56.654      0.000       0.269       0.288
lat             5.185e-05   1.24e-06     41.703      0.000    4.94e-05    5.43e-05
long           -5.475e-05   1.55e-05     -3.526      0.000   -8.52e-05   -2.43e-05
house_age          0.0049      0.000     37.609      0.000       0.005       0.005
renovation_age    -0.0062      0.006     -0.996      0.319      -0.019       0.006
coast_1            0.2775      0.035      7.948      0.000       0.209       0.346
sight_1.0          0.1768      0.020      8.793      0.000       0.137       0.216
sight_2.0          0.1467      0.012     11.938      0.000       0.123       0.171
sight_3.0          0.1769      0.017     10.527      0.000       0.144       0.210
sight_4.0          0.3144      0.025     12.423      0.000       0.265       0.364
zipcode_981        0.0591      0.007      8.751      0.000       0.046       0.072
furnished_1.0      0.0735      0.010      7.155      0.000       0.053       0.094
month_02           0.0320      0.015      2.064      0.039       0.002       0.062
month_03           0.0671      0.014      4.692      0.000       0.039       0.095
month_04           0.0903      0.014      6.513      0.000       0.063       0.117
month_05           0.0423      0.014      2.937      0.003       0.014       0.071
month_06           0.0230      0.015      1.515      0.130      -0.007       0.053
month_07           0.0314      0.015      2.066      0.039       0.002       0.061
month_08           0.0346      0.015      2.238      0.025       0.004       0.065
month_09           0.0063      0.016      0.407      0.684      -0.024       0.037
month_10           0.0160      0.015      1.031      0.303      -0.014       0.046
month_11           0.0082      0.016      0.504      0.615      -0.024       0.040
month_12           0.0177      0.016      1.102      0.271      -0.014       0.049
==============================================================================
Omnibus:                      127.077   Durbin-Watson:                   2.006
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              160.489
Skew:                           0.143   Prob(JB):                     1.41e-35
Kurtosis:                       3.417   Cond. No.                     1.15e+06
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.15e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


# initial list of columns
cols = x_train6.columns.tolist()

# setting an initial max p-value
max_p_value = 1

while len(cols) > 0:
    # defining the train set
    x_train_aux = x_train6[cols]

    # fitting the model
    model = sm.OLS(y_train, x_train_aux).fit()

    # getting the p-values and the maximum p-value
    p_values = model.pvalues
    max_p_value = max(p_values)

    # name of the variable with maximum p-value
    feature_with_p_max = p_values.idxmax()

    if max_p_value > 0.05:
        cols.remove(feature_with_p_max)
    else:
        break

selected_features = cols
print(selected_features)

['const', 'room_bed', 'room_bath', 'lot_measure', 'ceil', 'condition', 'quality', 'lat', 'long', 'house_age', 'coast_1', 'sight_1.0', 'sight_2.0', 'sight_3.0', 'sight_4.0', 'zipcode_981', 'furnished_1.0', 'month_03', 'month_04', 'month_05', 'month_07', 'month_08']


x_train6 = x_train5[selected_features]
x_test6 = x_test5[selected_features]


olsmod2 = sm.OLS(y_train, x_train6).fit()
print(olsmod2.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               logprice   R-squared:                       0.657
Model:                            OLS   Adj. R-squared:                  0.656
Method:                 Least Squares   F-statistic:                     1371.
Date:                Sun, 03 Apr 2022   Prob (F-statistic):               0.00
Time:                        19:26:54   Log-Likelihood:                -3305.5
No. Observations:               15083   AIC:                             6655.
Df Residuals:                   15061   BIC:                             6823.
Df Model:                          21                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
const             9.6687      0.037    261.125      0.000       9.596       9.741
room_bed          0.0243      0.004      6.868      0.000       0.017       0.031
room_bath         0.1739      0.006     31.467      0.000       0.163       0.185
lot_measure    3.216e-06   5.98e-07      5.379      0.000    2.04e-06    4.39e-06
ceil              0.0535      0.006      8.742      0.000       0.042       0.066
condition         0.0488      0.004     11.653      0.000       0.041       0.057
quality           0.2786      0.005     56.825      0.000       0.269       0.288
lat            5.183e-05   1.24e-06     41.708      0.000    4.94e-05    5.43e-05
long          -5.427e-05   1.55e-05     -3.496      0.000   -8.47e-05   -2.38e-05
house_age         0.0049      0.000     38.756      0.000       0.005       0.005
coast_1           0.2770      0.035      7.937      0.000       0.209       0.345
sight_1.0         0.1766      0.020      8.789      0.000       0.137       0.216
sight_2.0         0.1466      0.012     11.929      0.000       0.123       0.171
sight_3.0         0.1776      0.017     10.574      0.000       0.145       0.211
sight_4.0         0.3148      0.025     12.446      0.000       0.265       0.364
zipcode_981       0.0588      0.007      8.724      0.000       0.046       0.072
furnished_1.0     0.0730      0.010      7.109      0.000       0.053       0.093
month_03          0.0469      0.009      5.169      0.000       0.029       0.065
month_04          0.0701      0.008      8.361      0.000       0.054       0.086
month_05          0.0265      0.008      3.283      0.001       0.011       0.042
month_07          0.0173      0.008      2.058      0.040       0.001       0.034
month_08          0.0204      0.009      2.271      0.023       0.003       0.038
==============================================================================
Omnibus:                      127.664   Durbin-Watson:                   2.007
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              161.156
Skew:                           0.144   Prob(JB):                     1.01e-35
Kurtosis:                       3.417   Cond. No.                     1.76e+05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.76e+05. This might indicate that there are
strong multicollinearity or other numerical problems.


# let us create a dataframe with actual, fitted and residual values
df_pred = pd.DataFrame()

df_pred["Actual Values"] = y_train  # actual values
df_pred["Fitted Values"] = olsmod2.fittedvalues  # predicted values
df_pred["Residuals"] = olsmod2.resid  # residuals

df_pred.head(10)


# let's plot the fitted values vs residuals

sns.residplot(
    data=df_pred, x="Fitted Values", y="Residuals", color="purple", lowess=True
)
plt.xlabel("Fitted Values")
plt.ylabel("Residuals")
plt.title("Fitted vs Residual plot")
plt.show()


sns.histplot(data=df_pred, x="Residuals", kde=True)
plt.title("Normality of residuals")
plt.show()


import pylab
import scipy.stats as stats

stats.probplot(df_pred["Residuals"], dist="norm", plot=pylab)
plt.show()


stats.shapiro(df_pred["Residuals"]);

C:\Users\eadogla\Anaconda3\Anaconda1\lib\site-packages\scipy\stats\morestats.py:1681: UserWarning: p-value may not be accurate for N > 5000.
  warnings.warn("p-value may not be accurate for N > 5000.")


# predictions on the test set
pred = olsmod2.predict(x_test6)

df_pred_test = pd.DataFrame({"Actual": y_test, "Predicted": pred})
df_pred_test.sample(10, random_state=1)


df1 = df_pred_test.sample(25, random_state=1)
df1.plot(kind="bar", figsize=(15, 7))
plt.show()


# checking model performance on train set (seen 70% data)
print("Training Performance\n")
olsmod2_train_perf = model_performance_regression(olsmod2, x_train6, y_train)
olsmod2_train_perf

Training Performance


# checking model performance on test set (seen 30% data)
print("Test Performance\n")
olsmod2_test_perf = model_performance_regression(olsmod2, x_test6, y_test)
olsmod2_test_perf

Test Performance


# training performance comparison

models_train_comp_df = pd.concat(
    [linearregression_train_perf.T, olsmod2_train_perf.T], axis=1,
)

models_train_comp_df.columns = [
    "Linear Regression sklearn",
    "Linear Regression statsmodels",
]

print("Training performance comparison:")
models_train_comp_df

Training performance comparison:


# test performance comparison

models_test_comp_df = pd.concat(
    [linearregression_test_perf.T, olsmod2_test_perf.T], axis=1,
)

models_test_comp_df.columns = [
    "Linear Regression sklearn",
    "Linear Regression statsmodels",
]

print("Test performance comparison:")
models_test_comp_df

Test performance comparison:


olsmodel_final = sm.OLS(y_train, x_train6).fit()
print(olsmodel_final.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               logprice   R-squared:                       0.657
Model:                            OLS   Adj. R-squared:                  0.656
Method:                 Least Squares   F-statistic:                     1371.
Date:                Sun, 03 Apr 2022   Prob (F-statistic):               0.00
Time:                        19:27:30   Log-Likelihood:                -3305.5
No. Observations:               15083   AIC:                             6655.
Df Residuals:                   15061   BIC:                             6823.
Df Model:                          21                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
const             9.6687      0.037    261.125      0.000       9.596       9.741
room_bed          0.0243      0.004      6.868      0.000       0.017       0.031
room_bath         0.1739      0.006     31.467      0.000       0.163       0.185
lot_measure    3.216e-06   5.98e-07      5.379      0.000    2.04e-06    4.39e-06
ceil              0.0535      0.006      8.742      0.000       0.042       0.066
condition         0.0488      0.004     11.653      0.000       0.041       0.057
quality           0.2786      0.005     56.825      0.000       0.269       0.288
lat            5.183e-05   1.24e-06     41.708      0.000    4.94e-05    5.43e-05
long          -5.427e-05   1.55e-05     -3.496      0.000   -8.47e-05   -2.38e-05
house_age         0.0049      0.000     38.756      0.000       0.005       0.005
coast_1           0.2770      0.035      7.937      0.000       0.209       0.345
sight_1.0         0.1766      0.020      8.789      0.000       0.137       0.216
sight_2.0         0.1466      0.012     11.929      0.000       0.123       0.171
sight_3.0         0.1776      0.017     10.574      0.000       0.145       0.211
sight_4.0         0.3148      0.025     12.446      0.000       0.265       0.364
zipcode_981       0.0588      0.007      8.724      0.000       0.046       0.072
furnished_1.0     0.0730      0.010      7.109      0.000       0.053       0.093
month_03          0.0469      0.009      5.169      0.000       0.029       0.065
month_04          0.0701      0.008      8.361      0.000       0.054       0.086
month_05          0.0265      0.008      3.283      0.001       0.011       0.042
month_07          0.0173      0.008      2.058      0.040       0.001       0.034
month_08          0.0204      0.009      2.271      0.023       0.003       0.038
==============================================================================
Omnibus:                      127.664   Durbin-Watson:                   2.007
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              161.156
Skew:                           0.144   Prob(JB):                     1.01e-35
Kurtosis:                       3.417   Cond. No.                     1.76e+05
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.76e+05. This might indicate that there are
strong multicollinearity or other numerical problems.


# from sklearn.linear_model import LogisticRegression
from sklearn.tree import DecisionTreeRegressor
from sklearn.ensemble import (RandomForestRegressor
    )
from xgboost import XGBRegressor
from math import sqrt


from sklearn.metrics import mean_squared_error
from math import sqrt


model = RandomForestRegressor(random_state=1)
model.fit(x_train, y_train)

RandomForestRegressor(random_state=1)


model.score(x_train, y_train)

0.9812566573649877


model.score(x_test, y_test)

0.865013876206897


reg = RandomForestRegressor(criterion='mse')
reg.fit(x_train,y_train)
modelPred = reg.predict(x_train)
print(modelPred)

print("Number of predictions:",len(modelPred))

meanSquaredError=mean_squared_error(y_train, modelPred)
print("MSE:", meanSquaredError)
rootMeanSquaredError = sqrt(meanSquaredError)
print("RMSE:", rootMeanSquaredError)
MeanAbsoluteError =mean_absolute_error(y_train, modelPred)
print("MAE:", MeanAbsoluteError)
score2 = r2_score(y_train, modelPred)
print("R-squared:", score2)

[12.39725071 12.96574216 12.98125754 ... 12.88449609 14.10400459
 14.40625741]
Number of predictions: 15083
MSE: 0.00492639267146229
RMSE: 0.07018826591006712
MAE: 0.04978619597846937
R-squared: 0.9813544013436742


model = RandomForestRegressor(random_state=1)
model.fit(x_test, y_test)

RandomForestRegressor(random_state=1)


reg = RandomForestRegressor(criterion='mse')
reg.fit(x_test,y_test)
modelPred1 = reg.predict(x_test)
print(modelPred1)

print("Number of predictions:",len(modelPred1))
meanSquaredError=mean_squared_error(y_test, modelPred1)
print("MSE:", meanSquaredError)
rootMeanSquaredError = sqrt(meanSquaredError)
print("RMSE:", rootMeanSquaredError)
MeanAbsoluteError =mean_absolute_error(y_test, modelPred1)
print("MAE:", MeanAbsoluteError)
score2 = r2_score(y_test, modelPred1)
print("R-squared:", score2)

[12.50864242 12.90433714 13.16208593 ... 12.88387757 13.15586486
 13.94918612]
Number of predictions: 6465
MSE: 0.00537677194113592
RMSE: 0.07332647503552805
MAE: 0.05240194137096438
R-squared: 0.9796239368911762


DecisionTree = DecisionTreeRegressor(criterion='mse')
DecisionTree.fit(x_train,y_train)
modelPred = DecisionTree.predict(x_train)
print(modelPred)

print("Number of predictions:",len(modelPred))

meanSquaredError=mean_squared_error(y_train, modelPred)
print("MSE:", meanSquaredError)
rootMeanSquaredError = sqrt(meanSquaredError)
print("RMSE:", rootMeanSquaredError)
MeanAbsoluteError =mean_absolute_error(y_train, modelPred)
print("MAE:", MeanAbsoluteError)
score2 = r2_score(y_train, modelPred)
print("R-squared:", score2)

[12.35708842 12.98310131 12.95984445 ... 12.9456262  14.28551419
 14.41911199]
Number of predictions: 15083
MSE: 2.104744664790058e-09
RMSE: 4.5877496278568406e-05
MAE: 5.282881157191142e-07
R-squared: 0.9999999920338822


DecisionTree = DecisionTreeRegressor(criterion='mse')
DecisionTree.fit(x_test,y_test)
modelPred1 = DecisionTree.predict(x_test)
print(modelPred1)

print("Number of predictions:",len(modelPred1))
meanSquaredError=mean_squared_error(y_test, modelPred1)
print("MSE:", meanSquaredError)
rootMeanSquaredError = sqrt(meanSquaredError)
print("RMSE:", rootMeanSquaredError)
MeanAbsoluteError =mean_absolute_error(y_test, modelPred1)
print("MAE:", MeanAbsoluteError)
score2 = r2_score(y_test, modelPred1)
print("R-squared:", score2)

[12.48729641 12.88664104 13.36922346 ... 12.91164235 13.16590168
 13.99783211]
Number of predictions: 6465
MSE: 1.1274670942369914e-31
RMSE: 3.357777679116042e-16
MAE: 2.2255978962323324e-17
R-squared: 1.0


XGB =  XGBRegressor(criterion='mse')
XGB.fit(x_train,y_train)
modelPred = XGB.predict(x_train)
print(modelPred)

print("Number of predictions:",len(modelPred))

meanSquaredError=mean_squared_error(y_train, modelPred)
print("MSE:", meanSquaredError)
rootMeanSquaredError = sqrt(meanSquaredError)
print("RMSE:", rootMeanSquaredError)
MeanAbsoluteError =mean_absolute_error(y_train, modelPred)
print("MAE:", MeanAbsoluteError)
score2 = r2_score(y_train, modelPred)
print("R-squared:", score2)

[19:28:09] WARNING: C:/Users/Administrator/workspace/xgboost-win64_release_1.5.1/src/learner.cc:576: 
Parameters: { "criterion" } might not be used.

  This could be a false alarm, with some parameters getting used by language bindings but
  then being mistakenly passed down to XGBoost core, or some parameter actually being used
  but getting flagged wrongly here. Please open an issue if you find any such cases.


[12.446492 12.867141 12.84478  ... 12.904036 14.038291 14.464206]
Number of predictions: 15083
MSE: 0.011945975877843965
RMSE: 0.10929764808926112
MAE: 0.08090316651009587
R-squared: 0.9547864154096527


XGB =  XGBRegressor(criterion='mse')
XGB.fit(x_test,y_test)
modelPred1 = XGB.predict(x_test)
print(modelPred1)

print("Number of predictions:",len(modelPred1))
meanSquaredError=mean_squared_error(y_test, modelPred1)
print("MSE:", meanSquaredError)
rootMeanSquaredError = sqrt(meanSquaredError)
print("RMSE:", rootMeanSquaredError)
MeanAbsoluteError =mean_absolute_error(y_test, modelPred1)
print("MAE:", MeanAbsoluteError)
score2 = r2_score(y_test, modelPred1)
print("R-squared:", score2)

[19:28:10] WARNING: C:/Users/Administrator/workspace/xgboost-win64_release_1.5.1/src/learner.cc:576: 
Parameters: { "criterion" } might not be used.

  This could be a false alarm, with some parameters getting used by language bindings but
  then being mistakenly passed down to XGBoost core, or some parameter actually being used
  but getting flagged wrongly here. Please open an issue if you find any such cases.


[12.516713 12.858587 12.767736 ... 12.933366 13.148499 14.011458]
Number of predictions: 6465
MSE: 0.006747291388107428
RMSE: 0.08214189788474228
MAE: 0.05989277834893831
R-squared: 0.974430153139682


model = XGBRegressor(random_state=1)
model.fit(x_train, y_train)

XGBRegressor(base_score=0.5, booster='gbtree', colsample_bylevel=1,
             colsample_bynode=1, colsample_bytree=1, enable_categorical=False,
             gamma=0, gpu_id=-1, importance_type=None,
             interaction_constraints='', learning_rate=0.300000012,
             max_delta_step=0, max_depth=6, min_child_weight=1, missing=nan,
             monotone_constraints='()', n_estimators=100, n_jobs=8,
             num_parallel_tree=1, predictor='auto', random_state=1, reg_alpha=0,
             reg_lambda=1, scale_pos_weight=1, subsample=1, tree_method='exact',
             validate_parameters=1, verbosity=None)


model.score(x_train, y_train)  # Checking the train score

0.9547864154096527


model.score(x_test, y_test)  # Checking the test score

0.8800649215011859


# Import Linear Regression machine learning library
from sklearn.linear_model import LinearRegression
from sklearn.linear_model import Ridge
from sklearn.linear_model import Lasso

from sklearn.metrics import r2_score


ridge = Ridge(alpha=.1)
ridge.fit(x_train,y_train)
print ("Ridge model:", (ridge.coef_))

Ridge model: [-3.28710283e-02  6.85906706e-02  1.88450376e-04 -1.49892532e-05
  4.01555750e-02  5.66456287e-02  2.02960731e-01 -6.48013468e-06
 -4.74938288e-06  4.95396500e-05 -3.10020004e-05  1.32352226e-04
 -6.47609412e-06  1.48712814e-05  4.01161355e-03 -2.02558638e-02
  2.99593676e-01  1.09625586e-01  9.18474606e-02  1.04801444e-01
  2.16830674e-01  9.47924939e-02 -1.38921264e-02  2.84439749e-02
  6.47631646e-02  8.65087880e-02  3.01491307e-02  7.19120923e-03
  4.88116235e-03  1.68469717e-02 -8.21471556e-03 -3.78602534e-03
 -9.73194035e-03 -1.84060905e-03]


modelPred = ridge.predict(x_train)
print(modelPred)

print("Number of predictions:",len(modelPred))

meanSquaredError=mean_squared_error(y_train, modelPred)
print("MSE:", meanSquaredError)
rootMeanSquaredError = sqrt(meanSquaredError)
print("RMSE:", rootMeanSquaredError)
MeanAbsoluteError =mean_absolute_error(y_train, modelPred)
print("MAE:", MeanAbsoluteError)
score2 = r2_score(y_train, modelPred)
print("R-squared:", score2)

[12.74064427 12.83852916 12.71996899 ... 12.96228151 13.47558769
 14.36893839]
Number of predictions: 15083
MSE: 0.07916968182496571
RMSE: 0.28137107496145675
MAE: 0.22103218542174558
R-squared: 0.700355572220525


ridge = Ridge(alpha=.1)
ridge.fit(x_test,y_test)
print ("Ridge model:", (ridge.coef_))

Ridge model: [-3.22718823e-02  7.24833351e-02  1.60320837e-04 -3.27714735e-05
  4.89828190e-02  5.92605738e-02  2.00127351e-01 -1.01290745e-05
  2.91335916e-07  5.01649023e-05 -1.76700088e-05  1.47950549e-04
 -1.19625863e-06  2.82089546e-05  4.16070000e-03 -2.01479260e-02
  3.82245413e-01  1.53401037e-01  4.69767801e-02  1.31527396e-01
  1.22804738e-01  8.82006478e-02 -6.98536966e-04  3.58075900e-03
  5.22492568e-02  7.64543173e-02  4.14810506e-04 -1.61133805e-02
 -1.03735671e-02 -2.91999139e-02 -1.42795610e-02 -1.03711571e-02
 -2.25377270e-02 -5.24278043e-02]


modelPred = ridge.predict(x_test)
print(modelPred)

print("Number of predictions:",len(modelPred))

meanSquaredError=mean_squared_error(y_test, modelPred)
print("MSE:", meanSquaredError)
rootMeanSquaredError = sqrt(meanSquaredError)
print("RMSE:", rootMeanSquaredError)
MeanAbsoluteError =mean_absolute_error(y_test, modelPred)
print("MAE:", MeanAbsoluteError)
score2 = r2_score(y_test, modelPred)
print("R-squared:", score2)

[12.61448507 12.69763022 12.62225068 ... 12.77522765 13.18622413
 13.70986856]
Number of predictions: 6465
MSE: 0.07857386726569728
RMSE: 0.28031030531483725
MAE: 0.2192378487245761
R-squared: 0.702232846094649


lasso = Lasso(alpha=.1)
lasso.fit(x_train,y_train)
print ("Lasso model:", (lasso.coef_))

Lasso model: [-0.00000000e+00  0.00000000e+00  2.56653943e-04 -1.09413830e-05
  0.00000000e+00  0.00000000e+00  0.00000000e+00  1.02696248e-04
  8.02940139e-05  5.88108340e-05  6.46955716e-05  2.17521655e-04
 -8.36793671e-06  4.25365388e-06  2.97855990e-03 -0.00000000e+00
  0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
  0.00000000e+00  0.00000000e+00  0.00000000e+00 -0.00000000e+00
  0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
 -0.00000000e+00  0.00000000e+00 -0.00000000e+00 -0.00000000e+00
 -0.00000000e+00 -0.00000000e+00]


modelPred = lasso.predict(x_train)
print(modelPred)

print("Number of predictions:",len(modelPred))

meanSquaredError=mean_squared_error(y_train, modelPred)
print("MSE:", meanSquaredError)
rootMeanSquaredError = sqrt(meanSquaredError)
print("RMSE:", rootMeanSquaredError)
MeanAbsoluteError =mean_absolute_error(y_train, modelPred)
print("MAE:", MeanAbsoluteError)
score2 = r2_score(y_train, modelPred)
print("R-squared:", score2)

[12.79168258 12.90638014 12.82143015 ... 13.00536661 13.1875569
 14.29866973]
Number of predictions: 15083
MSE: 0.10474027256387435
RMSE: 0.3236360186442083
MAE: 0.25833528872749245
R-squared: 0.603575026267551


lasso = Lasso(alpha=.1)
lasso.fit(x_test,y_test)
print ("Ridge model:", (lasso.coef_))

Ridge model: [-0.00000000e+00  0.00000000e+00  2.49817177e-04 -2.77183272e-05
  0.00000000e+00  0.00000000e+00  0.00000000e+00  7.49911387e-05
  5.95666249e-05  6.01451996e-05  6.30800128e-05  2.39500916e-04
 -5.64163212e-06  1.85316303e-05  3.02958229e-03 -0.00000000e+00
  0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
  0.00000000e+00  0.00000000e+00  0.00000000e+00 -0.00000000e+00
  0.00000000e+00  0.00000000e+00  0.00000000e+00 -0.00000000e+00
  0.00000000e+00 -0.00000000e+00  0.00000000e+00 -0.00000000e+00
 -0.00000000e+00 -0.00000000e+00]

C:\Users\eadogla\Anaconda3\Anaconda1\lib\site-packages\sklearn\linear_model\_coordinate_descent.py:530: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.2990220716097838, tolerance: 0.17059640232656445
  model = cd_fast.enet_coordinate_descent(


modelPred = lasso.predict(x_test)
print(modelPred1)

print("Number of predictions:",len(modelPred1))

meanSquaredError=mean_squared_error(y_test, modelPred1)
print("MSE:", meanSquaredError)
rootMeanSquaredError = sqrt(meanSquaredError)
print("RMSE:", rootMeanSquaredError)
MeanAbsoluteError =mean_absolute_error(y_test, modelPred1)
print("MAE:", MeanAbsoluteError)
score2 = r2_score(y_test, modelPred1)
print("R-squared:", score2)

[12.516713 12.858587 12.767736 ... 12.933366 13.148499 14.011458]
Number of predictions: 6465
MSE: 0.006747291388107428
RMSE: 0.08214189788474228
MAE: 0.05989277834893831
R-squared: 0.974430153139682


feature_names = x_train.columns
importances = DecisionTree.feature_importances_
indices = np.argsort(importances)

plt.figure(figsize=(12, 12))
plt.title("Feature Importances")
plt.barh(range(len(indices)), importances[indices], color="violet", align="center")
plt.yticks(range(len(indices)), [feature_names[i] for i in indices])
plt.xlabel("Relative Importance")
plt.show()

	cid	dayhours	price	room_bed	room_bath	living_measure	lot_measure	ceil	...	basement	yr_built	yr_renovated	zipcode	lat	long	living_measure15	lot_measure15	total_area
2345	6450301690	20141003T000000	210000	3.0	1.00	1000.0	5454.0	1	...	0.0	1954	0	98133	47.7339	-122.337	1320.0	5250.0	6454
11333	4100000050	20141030T000000	813000	3.0	1.75	2080.0	11866.0	1	...	0.0	1960	0	98005	47.5872	-122.173	2240.0	10696.0	13946
12266	1370803820	20140602T000000	629000	3.0	2.00	1760.0	5000.0	1	...	800.0	1920	0	98199	47.6408	-122.403	1380.0	5000.0	6760
106	5127001620	20150211T000000	315000	3.0	1.75	1580.0	11455.0	1	...	380.0	1974	0	98059	47.4756	-122.147	1550.0	10650.0	13035
7002	3585210200	20140602T000000	366000	3.0	1.75	1510.0	8301.0	1	...	0.0	1967	0	98034	47.7243	-122.222	1460.0	7910.0	9811
7638	1934800133	20140711T000000	397500	3.0	2.50	1470.0	1256.0	2	...	540.0	2006	0	98122	47.6033	-122.309	1510.0	1797.0	2726
2077	6815100370	20141030T000000	845000	4.0	3.00	2390.0	4000.0	1.5	...	930.0	1931	0	98103	47.6857	-122.331	1670.0	4000.0	6390
17527	5420300240	20141205T000000	270000	3.0	1.75	1800.0	7763.0	1	...	330.0	1984	0	98030	47.3766	-122.184	1440.0	7483.0	9563
7342	2322069116	20140825T000000	530000	4.0	2.50	2690.0	46609.0	2	...	0.0	1980	1991	98038	47.3843	-122.006	1500.0	34800.0	49299
13479	4038200120	20140825T000000	534000	5.0	1.75	2120.0	8625.0	1	...	920.0	1959	0	98008	47.6118	-122.131	1930.0	8625.0	10745

	count	unique	top	freq	mean	std	min	25%	50%	75%	max
dayhours	21613	372	20140623T000000	142	NaN	NaN	NaN	NaN	NaN	NaN	NaN
price	21613.0	NaN	NaN	NaN	540182.158793	367362.231718	75000.0	321950.0	450000.0	645000.0	7700000.0
room_bed	21505.0	NaN	NaN	NaN	3.371355	0.930289	0.0	3.0	3.0	4.0	33.0
room_bath	21505.0	NaN	NaN	NaN	2.115171	0.770248	0.0	1.75	2.25	2.5	8.0
living_measure	21596.0	NaN	NaN	NaN	2079.860761	918.496121	290.0	1429.25	1910.0	2550.0	13540.0
lot_measure	21571.0	NaN	NaN	NaN	15104.583283	41423.619385	520.0	5040.0	7618.0	10684.5	1651359.0
ceil	21541.0	6.0	1.0	10647.0	NaN	NaN	NaN	NaN	NaN	NaN	NaN
coast	21582.0	2.0	0.0	21421.0	NaN	NaN	NaN	NaN	NaN	NaN	NaN
sight	21556.0	NaN	NaN	NaN	0.234366	0.766438	0.0	0.0	0.0	0.0	4.0
condition	21528.0	5.0	3.0	13978.0	NaN	NaN	NaN	NaN	NaN	NaN	NaN
quality	21612.0	NaN	NaN	NaN	7.656857	1.175484	1.0	7.0	7.0	8.0	13.0
ceil_measure	21612.0	NaN	NaN	NaN	1788.366556	828.102535	290.0	1190.0	1560.0	2210.0	9410.0
basement	21612.0	NaN	NaN	NaN	291.522534	442.58084	0.0	0.0	0.0	560.0	4820.0
yr_built	21598.0	116.0	2014.0	559.0	NaN	NaN	NaN	NaN	NaN	NaN	NaN
yr_renovated	21613.0	NaN	NaN	NaN	84.402258	401.67924	0.0	0.0	0.0	0.0	2015.0
zipcode	21613.0	NaN	NaN	NaN	98077.939805	53.505026	98001.0	98033.0	98065.0	98118.0	98199.0
lat	21613.0	NaN	NaN	NaN	47.560053	0.138564	47.1559	47.471	47.5718	47.678	47.7776
long	21579.0	752.0	-122.29	116.0	NaN	NaN	NaN	NaN	NaN	NaN	NaN
living_measure15	21447.0	NaN	NaN	NaN	1987.065557	685.519629	399.0	1490.0	1840.0	2360.0	6210.0
lot_measure15	21584.0	NaN	NaN	NaN	12766.54318	27286.987107	651.0	5100.0	7620.0	10087.0	871200.0
furnished	21584.0	NaN	NaN	NaN	0.19672	0.397528	0.0	0.0	0.0	0.0	1.0
total_area	21545.0	11144.0	6770.0	19.0	NaN	NaN	NaN	NaN	NaN	NaN	NaN

	dayhours	price	room_bed	room_bath	living_measure	lot_measure	ceil	condition	...	zipcode	lat	long	living_measure15	lot_measure15	furnished	total_area	year	month	day
14456	20150505T000000	550000	3.0	1.00	1070.0	3713.0	1.0	4.0	...	98118	47.5683	-122.285	1290.0	3960.0	0.0	4783.0	2015.0	05	05
4764	20140610T000000	1240000	5.0	3.00	2830.0	7500.0	2.0	3.0	...	98105	47.6579	-122.277	2900.0	5000.0	1.0	10330.0	2014.0	06	10
21581	20141019T000000	549950	3.0	1.75	2930.0	266587.0	2.0	3.0	...	98014	47.6991	-121.947	2700.0	438213.0	0.0	269517.0	2014.0	10	19
7816	20150402T000000	564450	3.0	2.50	2710.0	6174.0	2.0	3.0	...	98056	47.5120	-122.174	2730.0	7266.0	1.0	8884.0	2015.0	04	02
19573	20150410T000000	980000	5.0	4.00	3460.0	5400.0	2.0	3.0	...	98056	47.5201	-122.204	1890.0	5400.0	1.0	8860.0	2015.0	04	10
11817	20140714T000000	269950	3.0	2.50	1520.0	8720.0	1.0	3.0	...	98058	47.4267	-122.157	1720.0	7551.0	0.0	10240.0	2014.0	07	14
813	20141031T000000	474950	3.0	3.00	1530.0	1568.0	3.0	3.0	...	98117	47.6998	-122.367	1460.0	1224.0	0.0	3098.0	2014.0	10	31
11342	20141120T000000	616950	3.0	3.50	2490.0	2722.0	2.0	3.0	...	98005	47.5893	-122.165	2490.0	2755.0	0.0	5212.0	2014.0	11	20
2701	20140627T000000	504200	2.0	1.50	1200.0	1687.0	3.0	3.0	...	98103	47.6491	-122.334	1240.0	1296.0	0.0	2887.0	2014.0	06	27
15343	20140626T000000	243800	3.0	1.00	1140.0	7618.0	1.5	4.0	...	98027	47.5372	-121.972	1690.0	87300.0	0.0	28900.0	2014.0	06	26

	col	Adj. R-squared after_dropping col	RMSE after dropping col
0	basement	0.699698	0.281689
1	ceil_measure	0.699697	0.281689
2	total_area	0.699480	0.281791
3	lot_measure15	0.699199	0.281923
4	lot_measure	0.698905	0.282061
5	living_measure	0.689094	0.286619

	col	Adj. R-squared after_dropping col	RMSE after dropping col
0	ceil_measure	0.699717	0.281680
1	total_area	0.699499	0.281782
2	lot_measure15	0.699218	0.281914
3	lot_measure	0.698922	0.282053
4	living_measure	0.678388	0.291512

New missing rows found in coast and long¶

No missing value¶

Data Preprocessing (contd.)¶

Outlier Detection¶

Outlier Treatment¶

Linear Model Building¶

Linear Regression using statsmodels¶

Checking Linear Regression Assumptions¶

Removing Multicollinearity¶

TEST FOR LINEARITY AND INDEPENDENCE¶

Builing Alternative Models¶

Random Forest¶

Decision Tree¶

XGBoost¶

Ridge and Lasso¶

Conclusion¶

	price	room_bed	room_bath	living_measure	lot_measure	ceil	coast	sight	condition	quality	...	zipcode	lat	long	living_measure15	lot_measure15	furnished	total_area	year	month	day
0	600000	4.0	1.75	3050.0	9440.0	1	0	0.0	3	8.0	...	98034	47.7228	-122.183	2020.0	8660.0	0.0	12490	2015	04	27
1	190000	2.0	1.00	670.0	3101.0	1	0	0.0	4	6.0	...	98118	47.5546	-122.274	1660.0	4100.0	0.0	3771	2015	03	17
2	735000	4.0	2.75	3040.0	2415.0	2	1	4.0	3	8.0	...	98118	47.5188	-122.256	2620.0	2433.0	0.0	5455	2014	08	20
3	257000	3.0	2.50	1740.0	3721.0	2	0	0.0	3	8.0	...	98002	47.3363	-122.213	2030.0	3794.0	0.0	5461	2014	10	10
4	450000	2.0	1.00	1120.0	4590.0	1	0	0.0	3	7.0	...	98118	47.5663	-122.285	1120.0	5100.0	0.0	5710	2015	02	18
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
21608	685530	4.0	2.50	3130.0	60467.0	2	0	0.0	3	9.0	...	98014	47.6618	-121.962	2780.0	44224.0	1.0	63597	2015	03	10
21609	535000	2.0	1.00	1030.0	4841.0	1	0	0.0	3	7.0	...	98103	47.6860	-122.341	1530.0	4944.0	0.0	5871	2014	05	21
21610	998000	3.0	3.75	3710.0	34412.0	2	0	0.0	3	10.0	...	98075	47.5888	-122.04	2390.0	34412.0	1.0	38122	2014	09	05
21611	262000	4.0	2.50	1560.0	7800.0	2	0	0.0	3	7.0	...	98168	47.5140	-122.316	1160.0	7800.0	0.0	9360	2015	02	06
21612	1150000	4.0	2.50	1940.0	4875.0	2	0	0.0	4	9.0	...	98112	47.6427	-122.304	1790.0	4875.0	1.0	6815	2014	12	29

	dayhours	price	room_bed	room_bath	living_measure	lot_measure	ceil	coast	sight	condition	...	zipcode	lat	long	living_measure15	lot_measure15	furnished	total_area	year	month	day
0	20150427T000000	600000	4.0	1.75	3050.0	9440.0	1.0	0	0.0	3.0	...	980	7228.0	183.0	2020.0	8660.0	0.0	12490.0	2015.0	04	27
1	20150317T000000	190000	2.0	1.00	670.0	3101.0	1.0	0	0.0	4.0	...	981	5546.0	274.0	1660.0	4100.0	0.0	3771.0	2015.0	03	17
2	20140820T000000	735000	4.0	2.75	3040.0	2415.0	2.0	1	4.0	3.0	...	981	5188.0	256.0	2620.0	2433.0	0.0	5455.0	2014.0	08	20
3	20141010T000000	257000	3.0	2.50	1740.0	3721.0	2.0	0	0.0	3.0	...	980	3363.0	213.0	2030.0	3794.0	0.0	5461.0	2014.0	10	10
4	20150218T000000	450000	2.0	1.00	1120.0	4590.0	1.0	0	0.0	3.0	...	981	5663.0	285.0	1120.0	5100.0	0.0	5710.0	2015.0	02	18
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
21608	20150310T000000	685530	4.0	2.50	3130.0	60467.0	2.0	0	0.0	3.0	...	980	6618.0	962.0	2780.0	44224.0	1.0	63597.0	2015.0	03	10
21609	20140521T000000	535000	2.0	1.00	1030.0	4841.0	1.0	0	0.0	3.0	...	981	686.0	341.0	1530.0	4944.0	0.0	5871.0	2014.0	05	21
21610	20140905T000000	998000	3.0	3.75	3710.0	34412.0	2.0	0	0.0	3.0	...	980	5888.0	4.0	2390.0	34412.0	1.0	38122.0	2014.0	09	05
21611	20150206T000000	262000	4.0	2.50	1560.0	7800.0	2.0	0	0.0	3.0	...	981	514.0	316.0	1160.0	7800.0	0.0	9360.0	2015.0	02	06
21612	20141229T000000	1150000	4.0	2.50	1940.0	4875.0	2.0	0	0.0	4.0	...	981	6427.0	304.0	1790.0	4875.0	1.0	6815.0	2014.0	12	29

	Coefficients
room_bed	-0.032868
room_bath	0.068591
living_measure	0.000188
lot_measure	-0.000015
ceil	0.040152
condition	0.056646
quality	0.202966
ceil_measure	-0.000006
basement	-0.000005
lat	0.000050
long	-0.000031
living_measure15	0.000132
lot_measure15	-0.000006
total_area	0.000015
house_age	0.004012
renovation_age	-0.020253
coast_1	0.299871
sight_1.0	0.109682
sight_2.0	0.091869
sight_3.0	0.104831
sight_4.0	0.216835
zipcode_981	0.094793
furnished_1.0	-0.013901
month_02	0.028480
month_03	0.064801
month_04	0.086546
month_05	0.030186
month_06	0.007227
month_07	0.004917
month_08	0.016883
month_09	-0.008181
month_10	-0.003752
month_11	-0.009700
month_12	-0.001806
Intercept	10.911933

	feature	VIF
0	const	10888.632985
1	room_bed	1.784494
2	room_bath	3.382541
3	living_measure	78.411361
4	lot_measure	102.367933
5	ceil	2.394984
6	condition	1.259787
7	quality	4.540355
8	ceil_measure	68.115300
9	basement	19.337072
10	lat	1.076020
11	long	1.115272
12	living_measure15	3.112416
13	lot_measure15	6.097068
14	total_area	112.677988
15	house_age	2.488059
16	renovation_age	2.286239
17	coast_1	1.497023
18	sight_1.0	1.033328
19	sight_2.0	1.071585
20	sight_3.0	1.085488
21	sight_4.0	1.554001
22	zipcode_981	2.033645
23	furnished_1.0	2.941952
24	month_02	2.135019
25	month_03	2.657712
26	month_04	2.962044
27	month_05	3.445220
28	month_06	3.473643
29	month_07	3.541019
30	month_08	3.179320
31	month_09	3.117664
32	month_10	3.158380
33	month_11	2.653555
34	month_12	2.742412

	feature	VIF
0	const	10888.572113
1	room_bed	1.778702
2	room_bath	3.377510
3	living_measure	10.504693
4	lot_measure	100.755723
5	ceil	2.394899
6	condition	1.259787
7	quality	4.539320
8	ceil_measure	6.958951
9	lat	1.076020
10	long	1.114968
11	living_measure15	3.112390
12	lot_measure15	6.095961
13	total_area	110.862166
14	house_age	2.486116
15	renovation_age	2.286149
16	coast_1	1.496075
17	sight_1.0	1.032193
18	sight_2.0	1.069841
19	sight_3.0	1.083668
20	sight_4.0	1.550311
21	zipcode_981	2.033320
22	furnished_1.0	2.941806
23	month_02	2.134980
24	month_03	2.657648
25	month_04	2.962033
26	month_05	3.445141
27	month_06	3.473643
28	month_07	3.541002
29	month_08	3.179312
30	month_09	3.117551
31	month_10	3.158334
32	month_11	2.653555
33	month_12	2.742345

	feature	VIF
0	const	10884.748738
1	room_bed	1.778588
2	room_bath	3.305571
3	living_measure	7.146454
4	lot_measure	100.621014
5	ceil	1.824731
6	condition	1.248457
7	quality	4.539129
8	lat	1.074118
9	long	1.114939
10	living_measure15	3.078877
11	lot_measure15	6.093774
12	total_area	110.792870
13	house_age	2.486112
14	renovation_age	2.285042
15	coast_1	1.495842
16	sight_1.0	1.028893
17	sight_2.0	1.064728
18	sight_3.0	1.074528
19	sight_4.0	1.542749
20	zipcode_981	1.952309
21	furnished_1.0	2.878020
22	month_02	2.134321
23	month_03	2.657170
24	month_04	2.961551
25	month_05	3.444843
26	month_06	3.473530
27	month_07	3.541000
28	month_08	3.179312
29	month_09	3.117540
30	month_10	3.158233
31	month_11	2.653554
32	month_12	2.742270

	col	Adj. R-squared after_dropping col	RMSE after dropping col
0	total_area	0.699517	0.281774
1	lot_measure15	0.699236	0.281906
2	lot_measure	0.698937	0.282046
3	living_measure	0.669630	0.295455

	feature	VIF
0	const	10880.418483
1	room_bed	1.778302
2	room_bath	3.304552
3	living_measure	5.273102
4	lot_measure	5.975500
5	ceil	1.822484
6	condition	1.248378
7	quality	4.534300
8	lat	1.074087
9	long	1.113882
10	living_measure15	3.074662
11	lot_measure15	6.063573
12	house_age	2.486062
13	renovation_age	2.284503
14	coast_1	1.495819
15	sight_1.0	1.028411
16	sight_2.0	1.063731
17	sight_3.0	1.074426
18	sight_4.0	1.542671
19	zipcode_981	1.950877
20	furnished_1.0	2.877369
21	month_02	2.134275
22	month_03	2.657158
23	month_04	2.961455
24	month_05	3.444839
25	month_06	3.473515
26	month_07	3.540950
27	month_08	3.179273
28	month_09	3.117486
29	month_10	3.158226
30	month_11	2.653513
31	month_12	2.742236

	feature	VIF
0	const	10867.037487
1	room_bed	1.778251
2	room_bath	3.298463
3	living_measure	5.272664
4	lot_measure	1.650799
5	ceil	1.807879
6	condition	1.245025
7	quality	4.534270
8	lat	1.074040
9	long	1.112547
10	living_measure15	3.043073
11	house_age	2.481138
12	renovation_age	2.283017
13	coast_1	1.492258
14	sight_1.0	1.028142
15	sight_2.0	1.063673
16	sight_3.0	1.074417
17	sight_4.0	1.542671
18	zipcode_981	1.932974
19	furnished_1.0	2.874108
20	month_02	2.134267
21	month_03	2.657139
22	month_04	2.961333
23	month_05	3.444823
24	month_06	3.473477
25	month_07	3.540337
26	month_08	3.178874
27	month_09	3.117214
28	month_10	3.158001
29	month_11	2.652682
30	month_12	2.741682

	feature	VIF
0	const	10779.880398
1	room_bed	1.493063
2	room_bath	2.661444
3	lot_measure	1.508029
4	ceil	1.804666
5	condition	1.238593
6	quality	4.018332
7	lat	1.070900
8	long	1.109201
9	house_age	2.422876
10	renovation_age	2.274065
11	coast_1	1.491558
12	sight_1.0	1.019901
13	sight_2.0	1.050467
14	sight_3.0	1.062218
15	sight_4.0	1.528266
16	zipcode_981	1.836499
17	furnished_1.0	2.761618
18	month_02	2.134073
19	month_03	2.656629
20	month_04	2.960086
21	month_05	3.441877
22	month_06	3.466165
23	month_07	3.532445
24	month_08	3.175208
25	month_09	3.113771
26	month_10	3.152765
27	month_11	2.650655
28	month_12	2.738564

	Actual Values	Fitted Values	Residuals
148	12.357088	12.686241	-0.329152
6687	12.983101	12.851928	0.131173
7804	12.959844	12.686666	0.273178
8696	12.691580	12.849383	-0.157803
7133	12.323856	12.030367	0.293489
12439	13.035497	13.571691	-0.536194
6418	12.771386	13.118159	-0.346772
1357	12.988832	12.992292	-0.003460
21251	13.265598	12.680012	0.585586
8267	13.171154	12.812653	0.358500

	Actual	Predicted
16472	12.971540	12.851357
2118	12.860999	12.859185
18939	12.821258	12.854674
18062	12.983101	13.179958
8304	12.881565	12.935961
3428	13.647092	13.497250
7443	13.410545	13.078981
15304	13.180632	13.087140
4269	13.279367	12.939576
11307	13.693343	13.223619

	Linear Regression sklearn	Linear Regression statsmodels
RMSE	0.281371	0.301258
MAE	0.221032	0.236241
R-squared	0.700356	0.656501
Adj. R-squared	0.699679	0.655999
MAPE	1.698817	1.815106

	Linear Regression sklearn	Linear Regression statsmodels
RMSE	0.281515	0.300867
MAE	0.220163	0.235476
R-squared	0.699667	0.656958
Adj. R-squared	0.698079	0.655786
MAPE	1.693029	1.810472